Recent work on \(\gamma \) -ray emission models [1]} have shown that high values of \(\alpha \)  may not be necessary [2]}. A study of interpulse pulsars with high \(\dot{E}\)  [3]} showed that low emission heights are prevalent and that in many instances the beam is underfilled. In the work presented here, the measured values of \(\Delta \phi \)  also generally prefer low emission heights (below 500 km). These low emission heights coupled with large widths again imply low values of \(\alpha \)  via equation REF . We are therefore forced into the same conclusion as [4]} that either \(\alpha \)  is not randomly distributed or that emission occurs over a larger region than the classic polar cap extent. Indeed in a force-free magnetosphere the closed field-line region does not reach the light cylinder, thereby extending the region bounded by the open field lines (e.g. [5]}, [6]}, [7]}). Additional theoretical support for this idea based on the phenomenology of sub-pulse drifting can be found in [8]}.
